Carlton hit the nail on the head. The problem with line breeding is not the breeding itself, its the selection of offspring to become breeders! More on this in a moment.
First lets do a clarification of terms. Inbreeding refers to the breeding of very closely related animals, for several generations, causing problems in the offspring. It is a negative term for irresponsible breeding. Line breeding is the preferred term used by educated breeders who may occasionally breed related animals, but also introduce outside genetics to the line to keep it strong. IF line breeding is done correctly it can be done without any decrease in the health of the population. But you have to be very careful.
You also have to consider what a species is adapted to in the wild. Much of the scientific data we have about the dangers of inbreeding comes from laboratory bred mice. However mice are a fecund and widespread species that probably never evolved with closely related animals breeding on a regular basis. Certain reptiles may be very different. Take for example desert snakes from the southwestern US. Often you find small population hubs centered around a small piece of good habitat (a cliff face or stream bed for example) with many miles of poor habitat in between. These populations must be more able to deal with small gene pools or they would die out. They also must have some amount of gene flow between populations or they would evolve into different species or die out. I am not sure exactly where chams fall on this scale, but I would imagine there is a lot of species variability.
When you are considering captive populations you need to consider both the amount and the severity (for lack of better words). I.E. how closely related are the animals, and how many generations have they gone through without new gene introduction?
Breeding two closely related animals one time will not do anything bad unless you happen to be very unlucky and the parent animal is heterozygous for a dramatic genetic defect. This situation happens in nature all the time. As another person said, they don't know or care who their relatives are.
If you continue to only breed siblings (just an example) for many generations you will begin to see signs associated with inbreeding because you will increase the chances that individuals will carry multiple copies of a defective gene. These may be very subtle, like low hatch weight, or they may be dramatic birth defects.
So when and why do people do it? There are two different scenarios that are common and they are very different. Species like corn snakes and ball pythons have become popular due to the amount of mutations. These mutations are (usually) recessive which means that both parents must have the gene for the offspring to show the trait. This means that if you hatch out the first albino ball python ever, the ONLY way to get more of them is to breed it to its relatives. A good breeder will then out breed to maintain genetic diversity. But many people see the $$$$ and keep breeding closely related animals because it is the fastest way to get these traits without waiting for out breeding. No one would ever know until many generations later when the entire population has a problem. Specific diseases associated with morphs are known in many species.
Thankfully this is not the situation with chameleons. Chameleons are selectively bred for their colors over many generations (as opposed to a genetic mutation that appears suddenly). Therefore there is much less of a need to breed related animals. If you breed any two blue line panthers (related or not), the offspring have a good chance of being blue.
Coming full circle... the biggest issue is the selection of breeders. I don't care if you hatch out a panther that is bright yellow with purple polkadots, if its legs are wimpy and one eye is bigger than the other, DON"T BREED THAT ANIMAL!!!! And don't sell it to someone else with the intention of breeding it!
The reason inbreeding is less of a problem in the wild, is that if a breeding produces less fit animals, they will die off. In captivity it is up to us to ensure that the animals that go on to reproduce are fit. Those that are not can still make good pets but should not be bred. Select your hold backs by how well they feed and grow, not by the color of their skin, and you don't have to worry about mild line breeding to get pretty colors.
Stepping off soap box...